Nick Fitzgerald holds a well-diversified portfolio of high-quality, large-cap stocks. The current value of Fitzgerald's portfolio is $835,000, but he is concerned that the market is heading for a big fall (perhaps as much as 20% ) over the next three to six months. He doesn't want to sell all his stocks because he feels they all have good long-term potential and should perform nicely once stock prices have bottomed out. As a result, he's thinking about using index options to hedge his portfolio. Assume that the S\&P 500 currently stands at 2,854 and among the many put options available on this index are two that have caught his eye: (1) a six-month put with a strike price of 2,800 that's trading at $76.50, and (2) a six-month put with a strike price of 2,725 that's quoted at $57.50. a. How many S\&P 500 puts would Nick have to buy to protect his $835,000 stock portfolio? How much would it cost him to buy the necessary number of puts with a $2,800 strike price? How much would it cost to buy the puts with a $2,725 strike price? b. Now, considering the performance of both the put options and Nick's portfolio, determine how much net profit (or loss) Nick will earn from each c these put hedges if both the market (as measured by the S\&P 500) and Nick's portfolio fall by 15% over the next six months. What if the market and Nick's portfolio fall by only 5% ? What if they go up by 5% ? c. Do you think Nick should set up the put hedge and, if so, using which put option? Explain. d. Finally, assume that the DJIA is currently at 25,509 and that a six-month put option on the Dow is available with a strike price of 255 , and is a. The number of S\&P 500 puts Fitzgerald would have to buy to protect his $835,000 stock portfolio is put options. (Round up to the nearest whole number.)